Since GGMs and low-rank factorizations share a common root in structured covariance (or precision) matrix estimation, it appears desirable to leverage both approaches in a unified graph learning formulation.
On one hand, linear dimension reduction approaches rely on particular spectral structures that can be beneficial for graph learning [1]}.
On the other hand, it also opens the way to graph-oriented view of sparse principal component analysis [2]}, [3]}.
Though theoretically appealing, such unification is challenging because it formulates optimization problems with objective functions and constraints that apply both on the covariance matrix and its inverse.
Thus, deriving single-step learning algorithms for these models has only recently been addressed [4]}.
